Statistics Part I Hypothesis testing

• Descriptive statistics often relates to central tendency and variability in data sets
• Measures of central tendency relates to how the data collected is cultured on a graph and what this means in terms of our results
• Mode, Median, Mean are examples of central tendency
• Mode= most common
• Bimodal= 2 most common
• Median= middle observation in data
• Centre mass of data is the mean
• Equation of the mean

  A) Adding sum of all data

  B) Dividing sum by amount of data

  
• Measures of spread variability applies

  • Range
  • Inter-quartile range
  • Standard deviation
• Standardised units of common measure

  A) Standard deviation

  
• Standard deviation allows us to understand the spread and dispersion of our data, which helps in making predictions and drawing conclusions.
• A small standard deviation means that the data points are close to the mean, indicating that the values in the dataset are consistent and similar to each other.
• A large standard deviation, it tells us that the values in the dataset are more spread out and varied.
• Standard deviation

  A) How far away/ spread the data is from the mean

  
• A normal distribution symmetrically distributes data around the mean, forming a bell-shaped curve.
• Larger population size= closer the convergence to true population mean
• Normal distribution describes the average result found within the sample population
• The perfect parameters in a normal distribution are?

  Mode, median, mean= 0 and SD=1
• Standard deviation

  A) Standard deviation lengthens distribution

  
• Residual errors are the differences between observed and predicted values in a model.
• extrapolation and prediction are used within linear regression models
• Correlation describes the degree of association between two variables.
• Linear regression is for making predictions about the value of one variable (dependent) based on the value of another (independent) in future data
• What does this calculation represent?

  A) Mean

  
• The extreme bounds of the data relate to?

  The range

  A) highest-lowest range

  
• Focusing on the Central tendency distribution relates to the interquartile range

  A) 25%

  B) 25%

  
• The distribution of sample means will approach a normal distribution, regardless of the population's shape relates to The Central Limit Theorem
• Variability and variance are both measures of how spread out a single variable's values are.
• The data is reliable but often wrong which is defined as High Precision, High Bias
• The data is unreliable and often wrong, which can be defined as Low Precision, High Bias
• The data is reliable and mostly correct, which can be defined as High Precision and low Bias
• If data is unreliable but mostly correct we define it as low Precision, low bias:
• Precision describes the variability and bias is the central tendency
• The sample mean is can be defined as an unbiased estimate of the population mean

  
• The sample standard deviation is often termed as a biased estimate of the population standard deviation as it tends to underestimate the true value, especially for small sample sizes.

  
• We can fix sample standard deviation bias by increasing the sample size and applying the formula correction N-1

  
• When research only investigates an outcome variable, we often measure this through an observational design there is no independent manipulation
• When we think there's an effect but there's actually not; what type of error is this?

  Type I error
• When we think there's no effect but there's actually an effect; What type of error is this?

  Type II error
• We think there's no effect (Retain Null) x There's actually no effect (Null is true) leads us to conclude a true negative